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Stump the teach? The key of C♭ versus B

Hey Earle,
I’m reading my music theory book and it has a list for how many sharps and flats there are for each key. But there’s a C♭ key that has 7 flats, and a B key with 5 sharps. Why don’t they both have 5 or 7 accidental notes since they’re both going the same interval steps?

My student Nick emailed me this great question about keys. I had to take a moment and think of a tidy explanation. This seemingly simple question has a lot of depth and reveals a fundamental rule about keys. I thought I’d share the answer with you all of you.

First, let’s look at the key of C♭ and compare it to the key of C. The key of C has no sharps or flats, as in, each note is natural (neither sharp nor flat).

C D E F G A B C

The key of C♭ is one half step lower than the key of C. Not only is C♭ half step lower, but the other six notes are also a half step lower too. Therefore, all of the notes are flattened in the key of C♭, and thus the key of C♭ has seven flats.

I can guess what you’re thinking: aren’t Cb and B the same note? Yes, they are! So why do we have a different number of sharps (5) in the key of B than flats (7) in the key of C♭? The answer is a little complicated. It all boils down to a fundamental rule: we have to have one representative of each of the seven letters (A B C D E F G) in a key. Any of those letters can be modified with a sharp of flat so that the major key interval pattern (w w h w w w h) remains intact, but we need one of each. Let’s compare the two keys:

C♭ D♭ E♭ F♭ G♭ A♭ B♭ C♭

B C♯ D♯ E F♯ G♯ A♯ B

Notice that in the key of C♭, we give the name “C♭” to the note that we would normally refer to as “B.” Likewise, we give the name “F♭” to the note that we would normally refer to as “E.” However, in the key of B, we don’t use the alternative flat names for B and E. That is the disparity that we are talking about. If, in the key of Cb, we chose to leave “C♭” as “B” and “F♭” as “E”, we’d have two Bs and two Es represented and no C or F. That’s not allowed and it would look like this:

B D♭ E♭ E G♭ A♭ B♭ B

I hope you can see how that looks confusing. It is very clumsy to read, especially on sheet music. Consequently, it is rare to see the use of the key of Cb. Rather, the key of B is a cleaner way of describing that set of seven notes. There are no awkward C♭s or F♭s to deal with. The key of B is a better choice.

In summary, the key of B is cleaner and easier-to-read than C♭ because of the rule that we must have one of each letter represented in the key, and doing so from B eliminates the need of the awkward F♭ or C♭ notation.